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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 6, Pages 180–198 (Mi izv8298)  

This article is cited in 1 scientific paper (total in 1 paper)

High-frequency asymptotics of solutions of ODE in a Banach space

L. I. Sazonovab

a Southern Federal University, Rostov-on-Don
b South Mathematical Institute of VSC RAS

Abstract: We construct and justify high-frequency asymptotic expansions of solutions for some class of linear ODE in a Banach space. In particular, we obtain new results in the case when the averaged ODE are degenerate.

Keywords: periodic solution, differential equation, averaging, homogenization.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1 1398 2014 K
This paper was written within the framework of the project part of a state request in the sphere of scientific activity (task no. 1 1398 2014 K).


DOI: https://doi.org/10.4213/im8298

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English version:
Izvestiya: Mathematics, 2017, 81:6, 1234–1252

Bibliographic databases:

UDC: 517.928
MSC: 34G10, 34K33, 35B25, 35C20, 35K10, 47D06
Received: 17.09.2014
Revised: 09.09.2016

Citation: L. I. Sazonov, “High-frequency asymptotics of solutions of ODE in a Banach space”, Izv. RAN. Ser. Mat., 81:6 (2017), 180–198; Izv. Math., 81:6 (2017), 1234–1252

Citation in format AMSBIB
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  • https://doi.org/10.4213/im8298
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. R. Ishmeev, V. B. Levenshtam, “A system of partial differential equations with high-frequency coefficients and Stokes operator in the main part. Asymptotic integration in the case of multiple degeneration”, Russ. J. Math. Phys., 25:3 (2018), 284–299  crossref  mathscinet  zmath  isi  scopus
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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